The nuclear quadrupole hyperfine structure in rotational transitions of parent isotopomers of trichloroethylene, (Cl2C)-Cl-35=(CHCl)-Cl-35, and 1,1-dichloroethylene, (Cl2C)-Cl-35=CH2, was measured at sub-Doppler resolution with a pulsed supersonic beam, cavity Fourier transform microwave spectrometer. The complete inertial and principal nuclear quadrupole coupling tensors of all chlorine nuclei are determined. The three chlorine tensors for trichloroethylene have been assigned unambiguously to the structural positions of the chlorine nuclei on the basis of ab initio field gradient calculations. For both molecules the directions of the symmetry z axes of the field gradients at the chlorine nuclei show small, but significant, angular deviations delta from the directions of the respective CCl bonds. These differences are found to be well reproduced by ab initio calculations at the self-consistent field (SCF) level, with small sensitivity to the basis set. Similarly accurate reproduction of delta is demonstrated for various quadrupolar nuclei X=N, Cl, Br, and I terminal to CX bonds in several molecules. Consideration of contributions to the electric field gradient reveals that the small angular deviations delta reflect intermediate range molecular asymmetry about the bond axis to the measuring nucleus, at distances 1-4 Angstrom away. In the case of two neighboring atoms bonded to the same intermediate atom as the probe nucleus the direction of the z axis at this nucleus will, in general, deviate towards the neighbor with greater Z, and therefore, with greater local electron density.